Unformatted Digital Fiber-Optic Data Transmission for Radio Astronomy
Front-Ends
MATTHEW A. MORGAN
National Radio Astronomy Observatory, Charlottesville, VA 22903; matt.morgan@nrao.edu
J. RICHARD FISHER
National Radio Astronomy Observatory, Charlottesville, VA 22903; rfisher@nrao.edu
JASON J. CASTRO
National Radio Astronomy Observatory, Charlottesville, VA 22903; jcastro@nrao.edu
ABSTRACT. We report on the development of a prototype integrated receiver front-end that combines all
conversions from RF to baseband, from analog to digital, and from copper to fiber into one compact assembly, with
the necessary gain and stability suitable for radio astronomy applications. The emphasis in this article is on a novel
digital data link over optical fiber which requires no formatting in the front-end, greatly reducing the complexity,
bulk, and power consumption of digital electronics inside the antenna, facilitating its integration with the analog
components, and minimizing the self-generated radio-frequency interference (RFI) which could leak into the signal
path. Management of the serial data link is performed entirely in the back-end based on the statistical properties of
signals with a strong random noise component. In this way, the full benefits of precision and stability afforded by
conventional digital data transmission are realized with far less overhead at the focal plane of a radio telescope.
1. INTRODUCTION
Despite the widely recognized intrinsic value of
electronic component integration, most high-performance
radio astronomy front-ends today still retain the classical
boundaries between analog, digital, and optoelectronic subassemblies, limiting the degree to which the potential
benefits of system integration can ultimately be realized.
While each of these three sub-systems may themselves be
fully integrated, the interconnects that run between them
remain as one of the dominant sources of mechanical
failure, gain-frequency dependence, and gain instability in
the entire receiver chain.
We report on the development of a fully integrated
front-end comprising all non-cryogenic components of a
radio astronomy receiver, taking as its input a broadband
sky-frequency signal and delivering digital data at its output
on optical fiber, with all the necessary signal transformation
and conditioning in between (see Fig. 1). Successful
integration of all these functions – analog, digital, and
photonic – involves a number challenges. Prior publications
on this work have focused on the analog-digital design,
where the complementary natures of integration and digital
signal processing (that is, stability and precision) are
exploited to simplify front-end architecture while achieving
high levels of performance (Morgan & Fisher 2010;
Morgan, Fisher, & Boyd 2010; Morgan & Boyd 2011).
Special attention was paid to the integration of analog and
digital components in the front-end to ensure adequate
isolation of the sample clock and its harmonics.
With this article, we extend that work by incorporating
a novel digital fiber-optic transmission scheme which avoids
formatting of the data in the front-end – that is, it does not
use bit-scrambling, encoding, packetizing, or framing, nor
does it transmit meta-data of any kind, only raw samples.
This alleviates the potential problem of self-interference by
minimizing the digital electronics present in the antenna. It
also reduces the power consumption and bulk of the data
transmission system, facilitating its integration with the
analog components and the construction of large-format
focal-plane arrays.
Any implementation of a high-speed, serial data
transmission system must address the issues of DC balance,
clock recovery, and word alignment. Without transmitter
formatting, the approach taken in this work is to leverage
the known properties of the data itself, which for a radio
astronomy signal is well characterized by Gaussiandistributed white noise, even when strong interferers are
present. In this way, the overhead for management of the
serial data link is shifted entirely into the back-end. The
specific manner in which each of these issues is dealt with is
discussed in the following sections.
2. DC BALANCE
DC balance is needed because the components of a
high-speed serial link are usually AC-coupled. Any DC
offset is lost, resulting in a level shift in the eye diagram.
In the radio astronomy application, this is taken care of
automatically. Individual samples are random with
essentially a Gaussian probability distribution having zero
mean value, and inspection of the sample codes in either
two's-complement or straight/offset binary format, shown in
Fig. 2, reveals that they are anti-symmetric about the mid-
range; that is, positive sample codes are simply mirror
images of the negative sample codes wherein the 1's have
been replaced by 0's and vice-versa. These two facts
together ensure that each bit in any given sample has an
equal chance of being a 1 or a 0, and DC balance is
achieved. All that is required is that the ADC's have
reasonably low offset voltage. Minute offsets lead to
correspondingly minute vertical shifts in the eye diagram,
which are unlikely to break the serial link.
3. CLOCK RECOVERY
The conditions for successful clock recovery are
somewhat more difficult to articulate, and different
manufacturers will specify their requirements in different
ways. Some quote the number of consecutive identical
binary digits (presumably embedded in an otherwise
pseudo-random bit sequence) which can be tolerated by the
internal phase-locked loop, usually numbered in the
thousands. Other manufacturers calculate their spec in terms
of transition density, or the average number of bit changes
that occur over a large number of clock cycles. In either
case, conventional serial data links ensure that a sufficient
number of transitions are present for clock recovery by
employing bit scramblers.
For the radio astronomy application, the chances of raw
samples (or "words") from a Gaussian noise source
containing long strings of identical bits is vanishingly small.
Transition density may be calculated by counting the
number of transitions in each possible sample code and
summing them, each with a weight given by the (Gaussian)
probability of that sample code occurring,
(
)
(n + 1 )v − µ

erf σ2 20 + 1

(n − 1 )v − µ
pn = 12 
1 − erf σ2 20
(n + 12 )v0 − µ
(n − 12 )v0 − µ

erf
erf
−

σ 2
σ 2
(
( )
) ( )
n=0
n = 2 N − 1 (1)
otherwise
where n is the sample value, v0 is the sampler threshold
level, µ is the mean value of the signal relative to the bottom
of the reference scale, and σ is the standard deviation (rms,
or root-mean-square amplitude).
For the boundaries between samples, it is assumed for
the purposes of this analysis that the power spectrum of the
noise is white over the Nyquist bandwidth, ensuring that
adjacent samples are uncorrelated, although in practice this
assumption can be considerably relaxed. For zero-mean
noisy signals, this results in a bit transition at the word
boundary 50% of the time. If the ADC has an offset, then it
is necessary to consider the relative likelihood of sample
codes in the upper and lower half of the range, respectively,
in order to calculate the chances of a bit transition between
words. Primarily, this leads to a perturbation in the limiting
transition density at very low power levels.
The transition density as calculated in this manner is
shown in Fig. 3. The dotted line at 50% is a benchmark for
data streams having maximum entropy – that is, random
sequences for which knowledge of one bit provides no extra
information about what the next bit might be; it could be the
same or different with equal probability. This would be
typical of, say, a compressed data file. Higher transition
density than this aids in clock recovery, but such data
streams would be of diminishing value for efficient
communication, as beyond this point they become more
deterministic (100% transition density, for example, would
correspond solely to the fixed sequence of alternating 1's
and 0's). It is reasonable, therefore, to assume that
commercial clock recovery circuits should at least be able to
function with 50% transition density and probably a fair
amount less. Indeed, some datasheets indicate that 40% is
more than adequate.
It is evident from the plot that straight binary has an
advantage over two's complement in terms of its transition
density. This advantage becomes even more pronounced at
lower bit resolutions.
The open circles indicate the power levels where
optimum quantization efficiency would be achieved for the
specified number of bits (Thompson et. al. 2007). It is seen
that for both 4- and 8-bit sampling, this level corresponds
approximately to the peak in transition density. That the
optimal points fall close to the 50% maximum entropy line
may not be a coincidence, as quantization efficiency cannot
be independent of informational content.
For the present analysis, what matters most is that the
nominal operating points lie well within a regime where
clock recovery can be achieved without additional
formatting. Moreover, if 40% transition density represents a
safe lower bound for reliable operation, then the permissible
operating range for both 4- and 8-bits is roughly 23 dB
wide. (Later measurements suggest that 40% is much too
conservative, and that the link can be made to work over a
dynamic range that exceeds 50 dB.)
4. WORD ALIGNMENT
Upon successful recovery of the clock, the deserializer
in the back-end module of Fig. 1 begins transferring the
incoming data stream to its outputs in parallel format.
However, the boundaries between individual sample words
have been lost; the most-significant bit (MSB) from each
sample now appears at a random location on the deserializer
output pins. Word alignment is the process of detecting this
boundary and then rotating the data bits on the output pins
until the MSB appears in the correct location.
The mechanism for detecting the MSB is based on a
statistical calculation of the correlation between adjacent
bits. Inspection of the sample codes for straight binary
encoding (see Fig. 2) reveals that in the entire middle half of
the range the first and second most-significant bits are anticorrelated. The higher rate of occurrence of middle-half
sample codes given by the Gaussian distribution ensures
that these correlations will dominate in the data stream. The
remaining bits have alternating correlation and are
positively correlated in the most likely codes in the center.
In fact, if one assumes that the analog signal is Gaussiandistributed with a white power spectrum, the exact
probability of one bit being anti-correlated with its neighbor
may be calculated,
0 .5
 N −1− k
2
2 N −1 − 2 k (i − 12 )
qk = 
i −1
( −1) erf
v0
∑
σ 2
 i =1
(
)
k =0
1≤ k < N
(2)
where k=0 corresponds to the LSB and its adjacent bit is the
MSB from the next uncorrelated sample (Morgan and Fisher
2009 & 2011).
The result of this calculation for different bits in the
sample is plotted in Fig. 4. Note that the probability of anticorrelation for the MSB and the second most-significant bit
is close to unity for all power levels except where the signal
undergoes severe clipping at the rails (a condition which
will be referred to as inversion, for reasons that will soon
become clear). The same probability for any other bit pair is
always 50% or less. This serves as a statistical marker that
we can use to identify the MSB in the output words.
To do so, a single high-speed XOR gate is placed on the
two most-significant pins of the deserializer. If the word is
properly aligned, the output of the XOR gate (test point A in
Fig. 1) should be 1 almost all the time. If not, the output is a
1 only 50% of the time or less. This waveform is then
passed through an integrator or low-pass filter with a time
constant extending over thousands or millions of sample
periods, producing a DC voltage (test point B) which is
directly proportional to the duty cycle of the XOR output.
Finally, this voltage is checked against a pre-determined
threshold by a comparator, resulting in a logic output that
signals unambiguously when word alignment has been
achieved. It is up to the link management circuitry (in the
back-end) to trigger bit slips in the deserializer until word
alignment is indicated.
Note that beyond a root-mean-square input signal
amplitude of roughly 74% relative to the full-scale range of
the sampler, the probability advantage of the MSB is lost
and the algorithm fails. In Fig. 5, a comparison of the
histograms at nominal power levels and at this crossover
point helps to illustrate why this occurs. Recall that the
algorithm depended on the predominance of sample codes
in the middle half of the sampler range. At inversion, the
outermost bins at the rails of the sampler have accumulated
enough out-of-range samples that the integrated probability
of the signal falling in the outer two quadrants begins to
exceed 50% while that in the middle half drops below 50%.
The probability distribution function has then inverted.
5. MEASUREMENTS
A prototype integrated receiver was developed and
constructed according to Fig. 1 to verify these concepts. The
front-end module is shown in Fig. 6. It has an RF frequency
range of 1.2-1.7 GHz, with an instantaneous IF bandwidth
of roughly 75 MHz per sideband, 150 MHz total. The
ADC's have 8-bit resolution and are clocked at 155.5 MS/s
by a crystal oscillator source integrated into the module.
Both channels are connected to a 16-bit serializer driving a
low-power Vertical Cavity Surface Emitting Laser
(VCSEL). The fiber output is single-mode at 1310 nm
wavelength and operating at 2.488 Gbps serial data rate.
At the other end of the fiber is an evaluation back-end
consisting of an optical receiver board with built-in word
alignment circuitry and a 16-bit deserializer (see Fig. 7).
The parallel outputs are delivered by InfiniBand cable to a
National Instruments PXI-6562 data acquisition card. Three
visual LED monitors are provided on the back-end board for
diagnostic purposes. The first LED lights when the
photodiode is receiving an optical carrier. The second LED
is lit when the deserializer indicates that the serial clock has
been recovered. The final LED is tied to the output of the
comparator that indicates when word alignment has been
established. A pushbutton was provided to trigger the
SYNC input on the deserializer (initiating a single bit
rotation of the output word) but in practice it turned out to
be simpler to drive this input automatically from the data
acquisition computer.
The module was designed with appropriate gain for
radio astronomy applications, assuming that it is driven by
an external (usually cryogenic) amplifier. The initial tests,
however, were conducted without a preamp. Instead a
strong CW tone was injected directly into the RF port at 1
MHz offset from the local oscillator. In this way, sinusoidal
IF tones were synthesized in the front-end with a noise floor
almost too weak to be detected by the sampler. Although the
word alignment algorithm was designed to operate on the
Gaussian noise statistics that are typical of radio astronomy
data, all that is really required is that the sample codes in the
middle of the range are most frequent. Thus, a simple CW
tone works well so long as its amplitude is not too large, and
provides a means for easy visual inspection of the
deserialized data for verification (bit transmission errors in
essentially noisy data could very easily be missed.) The
resulting waveforms are shown in Fig. 8. Some dithering is
present which is attributed to residual noise in the front-end.
The different amplitudes of the sinusoids in the I and Q
channels resulting from gain mismatch is evident, as is the
expected quadrature phase relationship between the two.
Following this, an RF preamp was added to the
measurement setup in order to bring the noise floor up to
nominal levels (in an actual radio astronomy front-end, this
would correspond to the cryogenic gain inside the Dewar).
At first, the RF input of the preamp was terminated so that
the link may be tested with a noise-only input. Wordalignment was established, then data were recorded with the
digital output words rotated through each of the sixteen
possible positions to illustrate the appearance of the data in
both aligned and unaligned conditions. The results are
tabulated in Fig. 9. The first column describes the position
of the MSB as determined by the word alignment indicator.
The second and third columns are graphs of the time series
and frequency spectra for one of the two output channels.
Correct outputs are evident from the small amplitude of the
time series, and low-pass shape of the power spectrum.
Incorrect outputs appear much larger in amplitude and the
passband shape is lost. Note that valid data appears in the
first, ninth, and seventeenth row, corresponding to two
complete word rotations with the channels swapping places
once and then back again.
In the forth column is an oscilloscope trace taken at the
output of the XOR gate (test point A from Fig. 1). With the
words in proper alignment, this output is almost constant at
the logic-high level. The single downward spike in the
center of the trace on these rows corresponds to the rare
logic-low output that triggers the oscilloscope. After a single
bit-rotation, the trace changes to a predominately logic-low
output with occasional logic-high bits. In all other cases, the
duty cycle of the XOR output is on the order of 50%.
Finally, column five lists the DC voltage monitored at
the output of the integrator (test point B from Fig. 1). In
word-aligned position, the output is greater than 1 V. In all
other positions, it is below 20 mV. The threshold for the
comparator was set halfway between at 0.5 V.
Next, a CW tone was injected through the RF preamp
in order to simulate the effects of a strong non-Gaussian
source or interferer. Prior simulations had indicated that
such interferers, even when equal in power to the total
integrated noise in the band, only perturbed the probabilities
in Fig. 4 slightly, and this only at the right edge of the plot
where the sampler is near saturation (Morgan & Fisher 2009
and 2010). This test now confirms that result; nominal
operation of the serial link is unaffected by such an input.
The recorded time series and power spectra for both
channels are shown in Fig.'s 10 and 11. In these tests the
local oscillator was set to 1450 MHz, and the CW test tone
to 1475 MHz.
6. OPERATIONAL LIMITS
The final tests of the serial link involved running at
extreme analog power levels (both low and high) to
determine when clock recovery and word alignment would
fail, respectively.
As was indicated in Section 3, the transition density
needed for reliable clock recovery may not be achieved at
very low input power levels to the sampler, at which only
the innermost two sample codes occur frequently. For
straight binary encoding, the asymptotic transition density at
infinitesimal signal power and assuming zero offset in the
sampler is given by 1.5/N, where N is the number of bits per
sample. Interestingly, for samplers with small offsets the
limiting transition density actually improves to 2/N. Thus,
the minimum low-power transition density for 8-bit
sampling in straight binary is somewhere between 18-25%.
For fewer numbers of bits it is much larger.
In practice, one should expect clock recovery failure
due to low transition density to be a gradual phenomenon,
wherein momentary lapses in clock-to-data synchronization
cause bits to be lost or corrupted with increasing regularity.
An experiment was performed wherein the input noise
power to the prototype module was gradually reduced by
adjusting the preamp bias until the clock recovery loop
failed momentarily, allowing a bit to slip. A snapshot of the
data was recorded at each power level and the transitions
counted in order to verify the theory, as shown in Fig. 12.
(Minor deviations from the theoretical curve may result
from mis-estimation of the preamp's gain at low bias levels.)
The tests showed that an rms amplitude much less than a
single sampler threshold (less than 20% transition density in
this configuration) was required for the bit errors to occur
frequently enough that one could be observed in the 5minute time scale of the experiment – which, at 155.5 MS/s,
corresponds to a slip rate of approximately 1 out of every
1010 bits.
Importantly, further reduction in power does not make
the bit slips any more frequent than this – by that point the
sampler is only detecting zero-crossings and the statistics
relating to transition density cease to change (if anything,
the transition density would be on the rise again as a result
of the sampler offset phenomenon discussed above.) Also,
bit values were not being appreciably corrupted at this point
either, since that would tend to produce erratic sample codes
well outside the vanishingly small rms of the signal, and no
such outliers were observed.
It is interesting to note that while the clock recovery
circuit may fail intermittently at extremely low power levels
and large bit resolutions, manifesting as the infrequent loss
of one or more bits, Fig. 4 shows that the word alignment
algorithm should continue to work perfectly even down to
infinitesimal power levels. The system is therefore
automatically capable of detecting when it has missed a bit
and operation may continue in this state so long as it is
designed to monitor the status and re-align the word
boundaries when needed.
The final test was to increase the analog power level
until word alignment failed due to an excess of outerquadrant sample codes. Rather than further amplifying the
noise power, the amplitude of the CW tone was increased to
simulate the effects of a very strong interferer with nonGaussian characteristics – a far more likely scenario in
practice. The tests showed that with a nominal noise
amplitude of 15 levels rms, a CW power 14 times stronger
than the noise was required to invert the spectrum. The final
histogram at this break-point is shown in Fig. 13, along with
a theoretical model consisting of the convolution of
histograms for Gaussian and sinusoidal waveforms,
respectively. Asymmetry in the measured histogram is
probably the result of uneven compression in the analog
components prior to digitization.
Note that inversion of the probability density function
in this configuration occurs sooner than it would have for a
pure noise signal according to Fig. 4. This is due to the Ushaped histogram of a sinusoidal waveform. A strong CW
tone exhibits a predominance of outer-quadrant sample
codes at much lower power levels than pure Gaussian noise.
Still, the presence of a CW tone 14 times more powerful
than the integrated noise in the IF band is highly unlikely in
practice. Interestingly, adding more noise would likely
improve the reliability at these high power levels as it would
tend to restore the expected Gaussian profile to the
histogram.
7. FUTURE WORK
In this implementation of the receiver front-end, two
analog channels have been fed into the same serializer,
resulting in the samples from each channel being interleaved
within the data stream. This could be a common
configuration in real implementations, as many commercial
serializers operate on 16-bit words, and there is rarely any
reason for radio astronomy data to be digitized at such a
resolution. The word alignment algorithm described herein
has no way of determining which half of the 16-bit word
corresponds to the first channel and which corresponds to
the second, only that the first pin is the MSB of one of them.
There are a number of ways this could be handled at a
higher level using operational protocols. One is to note that
the analog outputs correspond to in-phase and quadraturechannels of a sideband separating mixer, so a calibration
signal (or other single-sideband observational source)
should have close to the expected +90 degree phase
correlation in the two channels; if it has the opposite sign
then the output words need to be swapped. Alternatively,
since the net gains of the independent analog channels will
almost certainly differ by a couple of dB, and the phase
relationship is to be calibrated post-construction anyway
(Morgan & Fisher 2010) one may simply adopt the
convention that the channel with the strongest amplitude
will always appear first on the deserializer output.
Also, although it was not attempted in this proof-ofconcept, many instrument architectures are likely to include
several links such as this in parallel corresponding to
different polarizations or different beams in a phased array,
where it may be important to track the relative propagation
delay between fiber channels. These delays may drift during
operation as a result of flexure on the cable wraps at the
telescope axes, or by thermal expansion over long distances.
This issue is quite familiar to engineers developing
analog fiber-optic links, and the solutions that might be
employed are quite similar, with one important exception:
The differential delay between any two recovered channels
in this scheme is discrete, corresponding to an integer
multiple of the sample length. In cross-correlation, the
relative phase between two channels would have a discrete
linear slope with respect to frequency, the possible values of
which may be predicted a-priori. Therefore, one needs only
to monitor and track the delay on separate fibers to within a
sample period, after which the correction for fiber-optic
delays will be exact.
Finally, the net power dissipation of all the noncryogenic analog, digital, and photonic components of a
radio astronomy front-end is quite substantial when
integrated into a single compact module such as this. The
current implementation draws 2.2 W of power – reasonably
efficient for a complete analog-digital-photonic subsystem,
but further reduction would be of great value in building
large focal plane arrays. Projections for higher-speed (10
Gbps) implementations are that they would require roughly
3.5-4.0 W of power, with almost half being dissipated in the
ADCs, and another quarter in the serializer.
The interface between the ADCs and the serializer is an
area where improvements could be made. Since the direct
connection of a very high-speed ADC and serializer is
unique to our design, the interface between these two
components using off-the-shelf parts is poorly optimized.
Anticipating that the samples from a high-speed ADC
would be clocked by some form of complex logic device or
micro-processor, the ADC outputs are typically delivered
off-chip using power hungry, transmission-line based,
differential logic protocols, such as Low-Voltage
Differential Signaling (LVDS). These bits are then gathered
by the serializer (in our application) using resistively
terminated LVDS receivers to be reformatted serially for
transfer to the laser driver, as shown in Fig. 14a. This entire
process is wasteful of power, pins, and circuit board real
estate. A better solution, shown in Fig. 14b, would be to
integrate both functions on to the same chip, avoiding the
need for off-chip resistor-loaded transmission-lines. It is
estimated that roughly a third of the ADC's power
dissipation and 10-15% of the total power budgeted for the
front-end could be saved at this interface alone. (Note that
the intent is for the serial output to run continuously in realtime at fiber-link serial data rates, say 2.5 Gbps or 10 Gbps,
distinguishing it from other serial-output ADCs which either
buffer their data for slower readout or deliver it on serial
LVDS lines at lower speeds along with synchronous serialand frame-rate clocks for immediate latching into a data
processor.)
It is also true that lower bit resolution, which is
acceptable in radio astronomy, could offer significant power
savings. Industrial applications, however, generally push for
greater bit resolution, limiting the availability of lower bit
resolution components. The lack of a parallel interface in
the proposed topology of Fig. 14b opens the door for
variable-resolution ADC architectures.
CONCLUSION
We have presented a complete, non-cryogenic front-end
receiver assembly for radio astronomy applications with all
the conversions from RF to baseband, from analog to
digital, and from copper to fiber in a single integrated
module. Key to the success of this module is a novel
unformatted fiber-optic link which minimizes the amount of
digital hardware required at the focal plane of the telescope,
reducing bulk and power dissipation while mitigating the
potential self-generated RFI. This enables large-format
focal-plane arrays to be constructed with in-situ digitization,
helping to confine the analog amplitude and phase drifts to
the integrated receiver where they are smallest, for
improved calibration longevity and performance.
Although the principles of operation are based on
Gaussian white noise, tests on the serial data link show that
it is robust and reliable in the presence of strong interferers
and real-world passbands. The implementations of both
front-end and back-end are simple and readily realizable
using off-the-shelf components (ADCs, serializers,
deserialiers, and high-speed logic gates). It is also scalable;
the prototype reported operates at a serial rate of 2.5 Gbps,
but extension to 10 Gbps is straightforward using available
components. Reduced power dissipation and wider analog
bandwidth commensurate with modern radio astronomy
requirements may be achieved using lower bit resolutions,
for which the link is even better suited (due to enhanced
transition density at low power levels.)
ACKNOWLEDGEMENTS
The authors would like to thank Bill Shillue, Francoise
Johnson, and Christophe Jacques for their help in
troubleshooting various aspects of this prototype. The
National Radio Astronomy Observatory is a facility of the
National Science Foundation operated under cooperative
agreement by Associated Universities, Inc.
REFERENCES
Morgan, M., & Fisher, J. 2010, PASP, 122, 326
———. 2009, NRAO Elec. Div. Tech. Note, #213
———. 2011, U.S. Patent Application 13/186739
Morgan, M., Fisher J., & Boyd, T. 2010, IEEE Trans.
Microwave Theory Tech., 58, 3666
Morgan, M., & Boyd, T. 2011, IEEE Trans. Microwave
Theory Tech., 59, 1214
Thompson, A., Emerson, D., & Schwab, F. 2007, Radio
Science, 42, RS3022
Fig. 1. Simplified block diagram of the prototype receiver using an I/Q mixer pair, including integrated analog-digital-photonic front-end
module and evaluation back-end with link-management components.
Fig. 2. Straight Binary and Two's Complement encoding of Gaussian distributed signals.
Fig. 3. Serial data transition density versus signal amplitude. The analog noise source is assumed to be Gaussian distributed with a white
power spectrum. Open circles represent levels that achieve optimum quantization efficiency, and the shaded regions represent nominal
operating ranges.
Fig. 4. Probability (qk) that bit k does not equal bit k-1, where k=0 corresponds to the least significant bit (LSB) and k=N-1 corresponds to
the most significant bit (MSB). This result is independent of bit-resolution.
Fig. 5. Comparison of sampler histograms where the signal power is either nominal or at inversion. Data shown for 8-bit resolution.
Fig. 6. Integrated analog-digital-photonic receiver front-end. Dimensions are 2.8" x 2.6" x 1.0".
Fig. 7. Evaluation back-end consisting of optical receiver with word alignment circuitry. The large IC in the center is the deserializer.
Board dimensions are 2.0" x 2.4".
Fig. 8. Quadrature sinusoid test signals after transmission over unformatted fiber optic link. Dithering is due to residual noise in the frontend.
Fig. 9. Output data for unformatted fiber optic link with broadband noise input.
Fig. 10. Time-series for both output channels with broadband noise and CW tone input.
Fig. 11. Power spectra for both output channels with broadband noise and CW tone input.
Fig. 12. Measured (markers) and modeled (solid line) transition density versus signal amplitude. The clock recovery loop failed
momentarily after roughly 5 minutes when the transition density dropped below 20%.
Fig. 13. Measured and modeled histogram with large-amplitude CW tone superimposed on broadband noise at the point where the word
alignment algorithm fails.
(a)
(b)
Fig. 14. Illustration of (a) conventional cascaded ADC and Serializer with LVDS ports, and (b) proposed combined ADC / Serializer with
variable bit-resolution.